Definition of The Gibbs Sampler: The Gibbs sampler is a way to generate empirical distributions of two variables from a model. Say the model defines probability distributions F(X|Y) and G(Y|X). Then start with a random set of possible X's, draw Y's from G(), then use those Y's to draw X's, and so on indefinitely. Keep track of the X's and Y's seen, and this will give samples enough to find the unconditional distributions of X and Y. (Econterms)

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